Question 142978
{{{x-2*sqrt(x)+1=0}}} Start with the given equation


Let {{{y=sqrt(x)}}}. So this means that {{{y^2=(sqrt(x))^2=x}}}



{{{y^2-2y+1=0}}} Replace {{{sqrt(x)}}} with {{{y}}} replace {{{x}}} with {{{y^2}}}




{{{(y-1)(y-1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{y-1=0}}} or  {{{y-1=0}}} 


{{{y=1}}} or  {{{y=1}}}    Now solve for y in each case



Since we have a repeating answer, our only answer is {{{y=1}}}



Remember, we let {{{y=sqrt(x)}}}


So this means that {{{sqrt(x)=1}}}


{{{x=1^2}}} Square both sides


{{{x=1}}} Simplify



So our answer is {{{x=1}}}